\newproblem{lay:1_9_37}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 1.9.37}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
	Let $T$ be a linear transformation whose standard matrix is given by $A=\begin{pmatrix} -5 & 6 & -5 & 6\\ 8 & 3 & -3 & 8\\2 & 9 & 5 & -12\end{pmatrix}$.
	Is $T$ a one-to-one transformation?
}{
  % Solution
	The standard matrix is row-equivalent to
	\begin{center}
		$\begin{pmatrix} 1 & 0 & 0 & 0.38\\ 0 & 1 & 0 & -0.32\\0 & 0 & 1 & -1.97\end{pmatrix}$
	\end{center}
	The transformation is not one-to-one (injective) because the columns of the standard matrix are not linearly independent (the fourth column can be expressed as
	$0.38\mathbf{a}_1-0.32\mathbf{a}_2-1.97\mathbf{a}_3$).
}
\useproblem{lay:1_9_37}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
